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Intersection of Quadrics in \(\mathbb {C}^n\), Moment-Angle Manifolds, Complex Manifolds and Convex Polytopes

  • Alberto VerjovskyEmail author
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2246)

Abstract

These are notes for the CIME school on Complex non-Kähler geometry from July 9th to July 13th of 2018 in Cetraro, Italy. It is an overview of different properties of a class of non-Kähler compact complex manifolds called LVMB manifolds, obtained as the Hausdorff space of leaves of systems of commuting complex linear equations in an open set in complex projective space \({\mathbb P}_{\mathbb {C}}^{n-1}\).

Notes

Acknowledgements

I would like to thank Yadira Barreto, Santiago López de Medrano, Ernesto Lupercio and Laurent Meersseman for their suggestions, lecture notes, and sharing their thoughts about the different aspects of the subject of these notes with me during several years. I would like to thank also the referee for pointing several typos and important mathematical details.

This work was partially supported by project IN106817, PAPIIT, DGAPA, Universidad Nacional Autónoma de México.

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Instituto de MatemáticasUniversidad Nacional Autónoma de México (UNAM)México CityMexico

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